Lee Bodzioch kept hearing that the economy was ­improving, so he redoubled his efforts to find a job, sending out résumés by the dozen and spending thousands of dollars to sharpen his technology skills in ­courses at Boston University.

But at age 57 — with decades of experience and professional connections — he feels shut out. After two years of unemployment, phone calls from prospective employers are increasingly rare. He has had one interview in the last seven months.

“Nothing is happening. Next to nothing,” said Bodzioch, of Billerica. “I don’t know what more I can do.”

Bodzioch is among those trapped in one of the most intractable problems facing the US economy — long-term unemployment — and older workers are being hit the hardest.

The number of people 45 and older who have been jobless for more than a year has quadrupled since 2007, accounting for nearly half of the 3.5 million Americans out of work for more than a year, according to the US ­Department of Labor.

“Historically, we’ve never seen anything that comes close to this; these numbers are unbelievably high,” said Andrew Sum, director of Northeastern University’s Center for Labor Market Studies. “And the longer you’re unemployed, the more likely you are to leave the labor force, and the more likely it’s an early retirement for you.”

This is not a sandy-beaches-and-sunsets type of retirement. After years of financial independence, many must lower standards of living, deplete savings, or rely on spouses’ earnings. The majority are older white men, according to the Labor Department, including many college-educated workers who rebounded from job losses earlier in their careers, only to see employment prospects dim in what should be their prime earning years.

The longer that people are unemployed, the harder it becomes for them to find work, economists say. Their skills atrophy or become outdated. They lose contacts and connections. They are viewed by prospective employers as damaged goods.

“It’s the problem I worry about the most,” said Nariman Behravesh, chief economist for IHS Global Insight, a Lexington forecasting firm. “We’re condemning these people, creating this permanent underclass.”

Here are three of their stories.

Prospects slipping away

Brian Cody of Ipswich was always able to land a job. In 1998, he left Digital Equipment Corp. in Maynard to work for an insurance company. He left there to work for the software company Sybase, but when sales slowed, he was laid off.

Cody rebounded quickly, getting a job as the marketing director at a business travel firm. And four years later, when the recession hit and he was laid off again, he thought he would rebound as he always had.

That was five years ago.

Now, 60, he still sends out résumés, scans job listings, and attends networking events. But with each passing day, he feels his prospects of ever working again are slipping away.

“I’ve been unable to get a sniff at any type of full-time employment at salaries not even half what I used to earn,” Cody said. “I worry constantly, but you just got to get up and plow ahead.”

In the first two years of unemployment, Cody went on scores of interviews, but said he never felt that he came close to landing a job. Typically, the interviewers were 20 years younger than he was, he said, and did not seem eager to “hire their dad.”

He still applies for jobs, but in recent years nearly all interest and phone calls from potential employers disappeared. Married for 37 years, the father of two adult children, Cody used to earn a six-figure salary. Last year, he landed just two job interviews.

“You draw your self-esteem from a number of different things, and one is your job,” Cody said. “To go through the interview process and find yourself rejected a number of times, well, you’ve got to have a strong sense of self not to come away damaged.”

Cody’s unemployment benefits ran out long ago, and he and his wife live off her income as a marketing consultant. He paints to pass the time and ease his frustration.

The most difficult part of being unemployed, he said, is convincing others he still has something to contribute to an employer, the economy, and society in general.

John McLaughlin has made a career out of repairing things, from heating boilers to computers. But the 59-year-old Wakefield resident has been unable to find a fix for his unemployment situation.

Two years ago, McLaughlin lost his job as manager of a Fidelity­ Investments call center when the company outsourced the work to India. He had worked at Fidelity for 16 years, but took the news in stride, confident he would land on his feet because of his high-tech experience.

“Then I started looking around and was like, ‘Whoa!’ ” he said. “I wasn’t getting any traction.”

Dozens of interviews later, McLaughlin’s spirits have slid downhill. He has applied for thousands of jobs, plenty for which he is overqualified. One prospective employer recently told him she wanted to hire him at half what he made at Fidelity, but was concerned he would quit if a better job came along. McLaughlin said he would not, and would be grateful for the job, but never heard back from the employer.

“After a while, you start to think, ‘Am I ever going to work again?’ ” said McLaughlin, a father with a marriage and mortgage. “But you have to block that out.”

It is an unhappy chapter after a lifetime of climbing the ladder. A graduate of Saugus High School, McLaughlin worked in the maintenance department of Saugus General Hospital, before taking an entry-level job at computer-maker Honeywell Information Systems in Billerica in 1982. Over 16 years at Honeywell, he rose to data center manager, but was laid off in 1995 when Groupe Bull of France took control of Honeywell and cut 800 jobs in Massachusetts.

The state and federal government paid $10,000 for McLaughlin to attend a 20-week retraining program at Boston University, where he learned computer support, service, and network skills. Within weeks of completion, he landed a job in Fidelity Investments’ information technology department. The job paid half of what he earned at Honeywell, but McLaughlin worked there for 16 years, until his layoff in 2011.

McLaughlin’s unemployment benefits ran out nearly a year ago. His wife, for many years a stay-at-home mom, supports them with her income as an office manager. McLaughlin takes care of the housekeeping and laundry, helps his adult children fix up their homes, and cares for his two Yorkies and a schnauzer.

His job search continues, he said, because this is not how his story is supposed to end.

“Life’s never been this way,” he said, struggling to find the right words. “It makes you feel . . . empty.”

Falling further behind

Lee Bodzioch completed an intensive 500-hour course in Web design, dipping deeper into dwindling savings to cover his $4,000 share for advanced skills training at Boston University’s Center for Digital Imaging Arts in Waltham. It was an investment he hoped would pay off with a job. It hasn’t, yet.

The empty silence that follows his job applications bothers him most. Typically, there’s not even a rejection letter telling him he did not get the job.

“If you hit your head against the wall it hurts,” Bodzioch said. “With a job search, there is nothing, no feedback, no reaction.”

The son of a sign painter in Adams, Bodzioch can barely remember another time when he was not working — whether helping his father hang lettered signs as a boy, or as an art director at Joslin Diabetes Center. He weathered layoffs during his 30-year career, always managing to reinvent himself by adapting to new technologies and updating his skills.

With a degree in fine art from Westfield State College, he designed printed annual reports for GenRad, a manufacturer of electronics equipment, until that company was bought by Teradyne in 2001 and he lost his job.

He responded by learning how to do design work on a computer, eventually landing a job with SimplexGrinnell, a fire safety company owned by Tyco International, but found himself out of a job again when the company moved its Massachusetts marketing offices to Boca Raton, Fla.

After a few months of unemployment, Bodzioch was hired by Joslin to create print and Web medical marketing materials. When that job disappeared because of changes in the law limiting pharmaceutical spending, Bodzioch found work several months later at a giant telecommunications company in Manchester, N.H., where he also created print and Web advertising for five years before he was laid off in early 2011.

Since then he has received only short-term contract work while managing to earn a little by playing drums in a band. Divorced with two adult children, Bodzioch said he is grateful that he has to support only himself.

His unemployment benefits barely cover his monthly car insurance bill, and he said he needs a job with health care benefits. He gets state-mandated health insurance through his unemployment benefits, but pays $18 a week for it.

He has not saved enough to retire, and with each passing week, he only falls further behind.

On good days, Bodzioch said, he may get calls from employment agencies alerting him to available jobs. He said he always applies, dreading the silence he has come to expect.